12.3.22 problem 23

Internal problem ID [1599]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 23
Date solved : Monday, January 27, 2025 at 05:13:08 AM
CAS classification : [_separable]

\begin{align*} \left (1+x \right ) \left (x -2\right ) y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 26

dsolve([(x+1)*(x-2)*diff(y(x),x)+y(x)=0,y(1) = -3],y(x), singsol=all)
 

\[ y = -\frac {3 \left (1+i \sqrt {3}\right ) 2^{{2}/{3}} \left (x +1\right )^{{1}/{3}}}{4 \left (x -2\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 23

DSolve[{(x+1)*(x-2)*D[y[x],x]+y[x]==0,y[1]==-3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3 \sqrt [3]{x+1}}{\sqrt [3]{4-2 x}} \]